This chapter discusses the development and implementation of algorithms based on Equation-Free/Dynamic Data Driven Applications Systems (EF/DDDAS) protocols for the computer-assisted study of the bifurcation structure of complex dynamical systems, such as those that arise in biology (neuronal networks, cell populations), multiscale systems in physics, chemistry and engineering, and system modeling in the social sciences. An illustrative example demonstrates the experimental realization of a chain of granular particles (a so-called engineered granular chain). In particular, the focus is on the detection/stability analysis of time-periodic, spatially localized structures referred to as "dark breathers". Results in this chapter highlight, both experimentally and numerically, that the number of breathers can be controlled by varying the frequency as well as the amplitude of an "out of phase" actuation, and that a "snaking" structure in the bifurcation diagram (computed through standard, model-based numerical methods for dynamical systems) is also recovered through the EF/DDDAS methods operating on a black-box simulator. The EF/DDDAS protocols presented here are, therefore, a step towards general purpose protocols for performing detailed bifurcation analyses directly on laboratory experiments, not only on their mathematical models, but also on measured data.

翻译：本章讨论了基于无方程/动态数据驱动应用系统（EF/DDDAS）协议的算法开发与实现，用于计算机辅助研究复杂动力系统的分岔结构。此类系统广泛存在于生物学（如神经元网络、细胞群体）、物理、化学与工程中的多尺度系统，以及社会科学中的系统建模。一个示例性案例展示了颗粒粒子链（即所谓的工程化颗粒链）的实验实现。特别地，本文聚焦于称为“暗呼吸子”的时间周期、空间局域化结构的检测与稳定性分析。本章结果从实验和数值两方面表明，呼吸子的数量可通过调节“异相”激励的频率和振幅进行控制；同时，通过标准、基于模型的动力系统数值方法计算得到的分岔图中的“蛇形”结构，也可通过基于黑箱模拟器运行的EF/DDDAS方法重现。本文提出的EF/DDDAS协议因此迈出了关键一步，旨在为直接在实验室实验（而非仅依赖其数学模型或实测数据）上执行详细分岔分析提供通用协议。